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About this book :-
Handbook of Ordinary Differential Equations: Exact Solutions, Methods, and Problems written by
Andrei D. Polyanin, Valentin F. Zaitsev
The Handbook of Ordinary Differential Equations for Scientists and Engineers, is a unique reference for scientists and engineers, which contains over 7,000 ordinary differential equations with solutions, as well as exact, asymptotic, approximate analytical, numerical, symbolic, and qualitative methods for solving and analyzing linear and nonlinear equations. First-, second-, third-, fourth- and higher-order ordinary differential equations and systems of equations are considered. A number of new nonlinear equations, exact solutions, transformations, and methods are described. Equations arising in various applications (in the theory of heat and mass transfer, nonlinear mechanics, elasticity, hydrodynamics, theory of nonlinear oscillations, combustion theory, chemical engineering science, etc.) are considered. Analytical formulas for the effective construction of solutions are given. Special attention is paid to equations of general form that depend on arbitrary functions. Almost all other equations contain one or more arbitrary parameters (i.e., in fact, this book deals with whole families of ordinary differential equations), which can be fixed by the reader at will. A number of specific examples where the methods described in the book are used are considered. Statements of existence and uniqueness theorems as well as theorems of stability and instability of solutions are given as well. Boundary-value problems and eigenvalue problems are described. Significant attention is given to Cauchy problems with blow-up solutions as well as the important questions of nonexistence and nonuniqueness of solutions to nonlinear boundary-value problems. Elements of bifurcation theory, Lie group and discrete-group methods for ODEs, and the factorization principle are discussed. Symbolic and numerical methods for solving ODEs problems with Maple, Mathematica, and MATLABr are considered.
This extensive handbook is the perfect resource for engineers and scientists searching for an exhaustive reservoir of information on ordinary differential equations.
(Andrei D. Polyanin, Valentin F. Zaitsev)
Book Detail :-
Title: Handbook of Ordinary Differential Equations: Exact Solutions, Methods, and Problems
Edition:
Author(s): Andrei D. Polyanin, Valentin F. Zaitsev
Publisher: Chapman and Hall/CRC
Series:
Year: 2018
Pages: 1487
Type: PDF
Language: English
ISBN: 1466569379,978-1-4665-6937-9
Country: Rassia
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About Author :-
The author Andrei D. Polyanin , D.Se., Ph.D., is a noted scientist of broad interests (ordinary differential, partial differential, and integral equations, mathematical physics, engineering mathematics, nonlinear mechanics, heat and mass transfer. chemical hydrodynamics, and others).
Andrei Polyanin graduated from the Department of Mechanics and Mathematics of the Moscow State University in 1974. He received his Ph.D. degree in 1981 and D.Se. degree in 1986 at the Institute for Problems in Mechanics of the Russian (former USSR) Academy of Sciences. Since 1975, Andrei Polyanin has been a member of the staff of the Institute for Problems in Mechanics of the Russian Academy of Sciences.
Professor Polyanin is an author of 21 books in English. Russian, German, and Bulgarian. His publications also include more than 120 research papers and three patents. In 1991, Andrei Polyanin was awarded a Chaplygin Prize of the USSR Academy of Sciences for his research in mechanics. E-mail: polyanin@ipmncLru
The author Valentin F. Zaitsev , Ph.D., D.Se., is a noted scientist in the fields of ordinary differential equations, mathematical physics, and nonlinear mechanics.
Valentin Zaitsev graduated from the Radio Electronics Faculty of the Leningrad Poly technical Institute (now Saint-Petersburg Technical University) in 1969 and received his Ph.D. degree in 1983 at the Leningrad State University. His Ph.D. thesis was devoted to the group approach to the study of some classes of ordinary differential equations. In 1992, Professor Zaitsev received his Doctor of Sciences degree; his D.Sc. thesis was dedicated to the discrete-group analysis of ordinary differential equations.
In 1971-1996, Valentin Zaitsev worked in the Research Institute for Computational Mathematics and Control Processes of the SL Petersburg State University. Since 1996. Professor Zaitsev has been a member of the staff of the Russian State Pedagogical University.
Professor Zaitsev has made important contributions to new methods in the theory of ordinary and partial differential equations. He is an author of more than 110 scientific publications. including 15 books and one patent. E-mail: z:lltsev@osipenko.stu.neva.ru
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Book Contents :-
Handbook of Ordinary Differential Equations: Exact Solutions, Methods, and Problems written by
Andrei D. Polyanin, Valentin F. Zaitsev
cover the following topics.
Preface
Authors
Basic Notation And Remarks
Part I. Methods for Ordinary Differential Equations
1 Methods for First-Order Differential Equations
2 Methods for Second-Order Linear Differential Equations
3 Methods for Second-Order Nonlinear Differential Equations
4 Methods for Linear ODEs of Arbitrary Order
5 Methods for Nonlinear ODEs of Arbitrary Order
6 Methods for Linear Systems of ODEs
7 Methods for Nonlinear Systems of ODEs
8 Elements of Bifurcation Theory
9 Elementary Theory of Using Invariants for Solving Equations
10 Methods for the Construction of Particular Solutions
11 Group Methods for ODEs
12 Discrete-Group Methods
Part II. Exact Solutions of Ordinary Differential Equations
13 First-Order Ordinary Differential Equations
14 Second-Order Ordinary Differential Equations
15 Third-Order Ordinary Differential Equations
16 Fourth-Order Ordinary Differential Equations
17 Higher-Order Ordinary Differential Equations
18 Some Systems of Ordinary Differential Equations
Part III. Symbolic and Numerical Solutions of Nonlinear PDEs with Maple, Mathematica, and MATLABr
19 Symbolic and Numerical Solutions of ODEs with Maple
20 Symbolic and Numerical Solutions of ODEs with Mathematica
21 Symbolic and Numerical Solutions of ODEs with MATLAB
Part IV.Supplements
S1 Elementary Functions and Their Properties
S2 Indefinite and Definite Integrals
S3 Tables of Laplace and Inverse Laplace Transforms
S4 Special Functions and Their Properties
References
Index
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